Electrophysiology generally involves placing electrodes into biological tissue of living organisms or into excised tissue. Common electrophysiological measurements are made in, e.g., brain or muscle tissue, but also other types of tissue may be subject to electrophysiological measuring. In the following, as an example, electrophysiological measurements in the brain are discussed. It is however to be noted that the described techniques are also applicable to other electrophysiological measurements.
A number of applications require a reliable method for detecting the activity of individual neurons. Examples include neural prostheses, where the activity of neurons in the cortex is measured and interpreted by a computer to control a prosthetic device. Another example would be functional neurosurgery, where recordings of neural activity are used to help refine the target location for surgical intervention. Additionally there are a number of research applications for which it is very important.
In order to measure activity from individual neurons, recordings are made with microelectrodes. A microelectrode is simply an electrode whose surface area is small enough to allow it to be selectively sensitive to only those neurons that are in its immediate vicinity. The activity of an individual neuron, as measured in this way, is typically a short, bipolar pulse called an action potential.
Microelectrode recordings typically consist of action potentials from a few nearby neurons (often referred to in the field as units), along with a strong noisy background. This background is a combination of averaged neural activity from large numbers of more distant neurons, and measurement noise due to, for example, impedance. As such, this background is typically broadband Gaussian noise.
The first steps to getting the activity of individual units are therefore to separate the action potentials from the background activity, and then separate the actions potentials into groups, where ideally each group represents a single unit. This process is called spike-sorting.
The very first step in spike-sorting is to find events in the data which are likely to represent an action potential. This is usually done by setting a threshold, and then defining the data in some interval immediately before and after any crossings of that threshold as an event. The background noise will occasionally cross the threshold due to chance, and the data may contain various artifacts that also cross the threshold. It is therefore extremely important that the threshold be optimally set for the data. The optimal setting being one for which a minimal number of action potentials are missed, and a minimal number of false-positives are found.
A critical step in setting the threshold for spike detection is to estimate the amplitude of the background noise. If one knows (or can assume) that the background noise is normally distributed, then one can set the threshold to a level such that false-positives due to random chance are very uncommon. Estimating the noise amplitude for microelectrode recordings can be a very tricky task, though. While the background noise itself is typically very accurately modeled as broad-band Gaussian noise, other activity such as action potentials and artifacts can also account for a large portion of the measured data, which makes the task of reliably estimating the noise distribution very difficult.
The most straight-forward way to estimate the noise amplitude is to measure the standard deviation of the overall signal. If the signal consists almost entirely of just noise, then this can be quite accurate. Unfortunately, the standard deviation is extremely sensitive to the presence of outliers. The standard deviation is especially sensitive to extreme outliers, meaning that if the action potentials or artifacts present in the signal have amplitudes much larger than the noise level, then even a small fraction of the data being contaminated can have a substantial effect on the standard deviation of the resulting signal.
A more robust method for estimating the noise-level is described in “Unsupervised Spike Detection and Sorting with Wavelets and Superparamagnetic Clustering” by Quian Quiroga, Nadasdy and Ben-Shaul (2004). This method uses the median of the absolute value of the signal, and divides it by a constant factor (0.6745). This method is based on the observation that for Gaussian noise, the median of the absolute value of the signal is proportional to the standard deviation of the signal. Generally speaking, the median of a distribution is far more robust to the presence of outliers than the standard deviation is, particularly when the outliers have much larger amplitudes than the noise. In fact, the median is not really sensitive to the amplitude of the outliers at all. The only factor that it is sensitive to is the fraction of the data that is contaminated.
In the case of zero mean Gaussian noise the median is also zero, and does not depend at all on the noise amplitude. Therefore, in the median estimation method of Quian Quiroga et al., the absolute value of the measured signal is used. The median estimate method performs much better than the method based on a direct measurement of the signal's standard deviation, especially for higher firing rates (frequency of occurrence of events in a simulated sample signal). However, even the improved estimate overestimates the noise amplitude by about 20% for a firing rate of 100 Hz.